Related papers: Dos and don'ts of reduced chi-squared
Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least…
It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is, in large part, Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information…
The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to…
Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…
Error-in-variables regression is a common ingredient in treatment effect estimators using panel data. This includes synthetic control estimators, counterfactual time series forecasting estimators, and combinations. We study high-dimensional…
Previously, we derived exact relationships between the properties of a linear time-invariant control system and properties of an anomaly detector that quantified the impact an attacker can have on the system if that attacker aims to remain…
For linear models with spatial errors, the empirical likelihood ratio statistics are constructed for the parameters of the models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared…
The classic chi-squared statistic for testing goodness-of-fit has long been a cornerstone of modern statistical practice. The statistic consists of a sum in which each summand involves division by the probability associated with the…
Neutrino disappearance measurements using binned reconstructed-energy spectra exhibit a regime in which small mass-squared splittings become unidentifiable at quadratic order when smooth spectral shape uncertainties are represented by…
Estimating errors is a crucial part of any scientific analysis. Whenever a parameter is estimated (model-based or not), an error estimate is necessary. Any parameter estimate that is given without an error estimate is meaningless.…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
We examine the errors on counts in cells extracted from galaxy surveys. The measurement error, related to the finite number of sampling cells, is disentangled from the ``cosmic error'', due to the finiteness of the survey. Using the…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
Telescopes are much more expensive than astronomers, so it is essential to minimize required sample sizes by using the most data-efficient statistical methods possible. However, the most commonly used model-independent techniques for…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined in a restricted space. It can also be…
We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman's and Pearson's chi-squares, namely "combined Neyman-Pearson chi-square" ($\chi^2_{\mathrm{CNP}}$). Through analytical…
Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…
The method of obtaining confidence intervals on a subset of the total number of parameters (p) of a model used for fitting X-ray spectra is to perturb the best-fitting model until, for each parameter, a range is found for which the change…